Problem: $\dfrac{ -u - 7v }{ -7 } = \dfrac{ 10u - 4w }{ 7 }$ Solve for $u$.
Explanation: Notice that the left- and right- denominators are opposite $\dfrac{ -u - 7v }{ -{7} } = \dfrac{ 10u - 4w }{ {7} }$ So we can multiply both sides by $-7$ $-{7} \cdot \dfrac{ -u - 7v }{ -{7} } = -{7} \cdot \dfrac{ 10u - 4w }{ {7} }$ $-u - 7v = - \cdot \left( 10u - 4w \right) $ Distribute the negative sign on the right side. $-u - 7v = -10u + 4w$ $-{1}u - {7}v = -{10}u + {4}w$ Combine $u$ terms on the left. $-{u} - 7v = -{10u} + 4w$ ${9u} - 7v = 4w$ Move the $v$ term to the right. $9u - {7v} = 4w$ $9u = 4w + {7v}$ Isolate $u$ by dividing both sides by its coefficient. ${9}u = 4w + 7v$ $u = \dfrac{ 4w + 7v }{ {9} }$